Skip to main content
SpringerLink
Log in

On pseudo BL-algebras with internal state

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The scope of this paper is to put in evidence some characteristics and properties of the operations with state filters of a pseudo BL-algebra with internal state. I define the concepts of maximal and prime state filter of a state pseudo BL-algebra, I characterize a maximal state filter and I prove a Prime state filter theorem. Also, I characterize the state-filters algebra of a state pseudo BL-algebra.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Balbes R, Dwinger P (1974) Distributive lattices, XIII. University of Missouri Press, Columbia

  • Blok WJ, Pigozzi D (1989) Algebraizable logics. Memoirs of the American Mathematical Society, No. 396. Amer. Math. Soc., Providence

  • Ciungu LC, Dvurečenskij A, Hyčko M (2011) State BL-algebras. Soft Comput. 15:619–634

    Article  MATH  Google Scholar 

  • Constantinescu NM (2010) A note on BL-algebras with internal state. Ann Univ Craiova Math Comp Sci Ser 33(3):116–129

    MathSciNet  Google Scholar 

  • Di Nola A, Georgescu G, Iorgulescu A (2002a) Pseudo BL-algebras: part I. Multiple Valued Logic 8(5–6):673–714

    MathSciNet  MATH  Google Scholar 

  • Di Nola A, Georgescu G, Iorgulescu A (2002b) Pseudo BL-algebras: part II. Multiple Valued Logic 8(5–6):717–750

    MathSciNet  MATH  Google Scholar 

  • Dvurečenskij A, Rachůnek J, Šalounová D (2012) State operators on generalizations of fuzzy structures. Fuzzy Sets Syst 187:58–76

    Article  MATH  Google Scholar 

  • Flaminio T, Montagna F (2009) MV-algebras with internal state and probabilistic fuzzy logics. Int J Approx Reason 50:138–152

    Article  MathSciNet  MATH  Google Scholar 

  • Iorgulescu A (2008) Algebras of logic as BCK algebras. Editura ASE, Bucharest

  • Kühr J (2003) Pseudo-BL algebras and DRL-monoids. Math Bohem 128:199–208

    MathSciNet  MATH  Google Scholar 

  • Mureşan C (2009) Algebras of Many-valued logics. Ph. D. Thesis, University of Bucharest

  • Piciu D (2007) Algebras of fuzzy logic. Ed. Universitaria, Craiova

  • Rachůnek J, Šalounová D (2011) State operators on GMV-algebras. Soft Comput 15:327–334

    Article  MATH  Google Scholar 

  • Turunen E (1999) Mathematics behind fuzzy logic. Advances in soft computing. Physica-Verlag, Heidelberg

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Craiova, Al. I. Cuza Street, 13, 200585, Craiova, Romania

    N. M. Constantinescu

Authors
  1. N. M. Constantinescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. M. Constantinescu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Constantinescu, N.M. On pseudo BL-algebras with internal state. Soft Comput 16, 1915–1922 (2012). https://doi.org/10.1007/s00500-012-0864-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-012-0864-y

Keywords

Search

Navigation